The HST's WFPC2 has several advantages over ground--based observations for the study of globular cluster luminosity functions (GCLFs) and distance determination. Here we present WFPC2 data on the globular clusters associated with NGC 5846. This giant elliptical is the dominant galaxy in a small, compact group located 13 Mpc beyond the Virgo cluster. We have detected over 1200 globular clusters in three (central, north and south) separate pointings. The luminosity function in each of these

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... ngs are statistically the same, indicating that the mean luminosity (mass) does not vary between 3 and 30 kpc from the galaxy center. This suggests that dynamical friction and bulge shocking destruction processes are insignificant. We have fit a Gaussian and t_5 profile to the GCLF (of the combined pointings) and find that it is well represented by a turnover magnitude of m^0_V = 25.05 +/- 0.10 and a dispersion of sigma = 1.34 +/- 0.06. Our 50 the turnover. After applying a metallicity correction to the 'universal' GCLF turnover magnitude, we derive a distance modulus of (m--M) = 32.32 +/- 0.23. For a group velocity V_CMB = 1883 +/- 28 km/s, the Hubble constant is H_o = 65 +/- 8 km/s/Mpc.